Under the condition of weak waveguiding, the effect of index gradual change is considered. The gradient index ∇ε as perturbation term is introduced in the scalar Helmholtzequation, and the perturbation method is used to solve the problem of triangular-profile gradient index single-mode fiber, which can shift the dispersion minimum from the wave length 1.31μm to 1.55μm. The first order correct solution is given with an integral form and numerical results calculated by integral expression are also given.

A Scalar wave equation with an aix direction variate z is used to describe a single-mode taper fiber, and the scalar wave equation is changed to one-order differential equations group by a Simple transform. The quartic Runge-kutta Method improved by Gill is used to Calculate the propagation Characters of a Single-mode taper fiber.